English
Related papers

Related papers: Cartan calculus in string topology

200 papers

The c-map relates classical hypermultiplet moduli spaces in compactifications of type II strings on a Calabi-Yau threefold to vector multiplet moduli spaces via a further compactification on a circle. We give an off-shell description of the…

High Energy Physics - Theory · Physics 2009-11-11 Martin Rocek , Cumrun Vafa , Stefan Vandoren

We study the spaces of string links and homotopy string links in an arbitrary manifold using multivariable manifold calculus of functors. We construct multi-cosimplicial models for both spaces and deduce certain convergence properties of…

Algebraic Topology · Mathematics 2009-11-03 Brian A. Munson , Ismar Volic

We derive a map relating the gauge symmetry groups of heterotic strings on $T^4$ to other components of the moduli space with rank reduction. This generalizes the results for $T^2$ and $T^3$ which mirror the singularity freezing mechanism…

High Energy Physics - Theory · Physics 2022-08-25 Bernardo Fraiman , Héctor Parra de Freitas

Arone and Turchin defined graph-complexes computing the rational homotopy of the spaces of long embeddings. The graph-complexes split into a direct sum by the number of loops in graphs. In this paper we compute the homology of its two-loop…

Algebraic Topology · Mathematics 2013-10-08 Jim Conant , Jean Costello , Victor Tourtchine , Patrick Weed

A loop is a rather general algebraic structure that has an identity element and division, but is not necessarily associative. Smooth loops are a direct generalization of Lie groups. A key example of a non-Lie smooth loop is the loop of unit…

Differential Geometry · Mathematics 2020-08-20 Sergey Grigorian

Let M be a smooth, simply-connected, closed oriented manifold, and LM the free loop space of M. Using a Poincare duality model for M, we show that the reduced equivariant homology of LM has the structure of a Lie bialgebra, and we construct…

Algebraic Topology · Mathematics 2015-05-13 Xiaojun Chen , Farkhod Eshmatov , Wee Liang Gan

By studying spaces of flow graphs in a closed oriented manifold, we construct operations on its cohomology, parametrized by the homology of the moduli spaces of compact Riemann surfaces with boundary marked points. We show that the…

Geometric Topology · Mathematics 2013-05-03 Viktor Fromm

We discuss the appearance of modular functions at the one-loop gauge and gravitational couplings in (0,2) non-decomposable N=1 four dimensional orbifold compactifications of the heterotic string. We define the limits for the existence of…

High Energy Physics - Theory · Physics 2010-11-19 Christos Kokorelis

We calculate mod-p cohomology of extended powers, and their group completions which are free infinite loop spaces. We consider the cohomology of all extended powers of a space together and identify a Hopf ring structure with divided powers…

Algebraic Topology · Mathematics 2023-07-04 L. Guerra , P. Salvatore , D. Sinha

Configuration space integrals have in recent years been used for studying the cohomology of spaces of (string) knots and links in $\mathbb{R}^n$ for $n>3$ since they provide a map from a certain differential algebra of diagrams to the…

Algebraic Topology · Mathematics 2017-11-16 Robin Koytcheff , Brian A. Munson , Ismar Volic

We study string topology for classifying spaces of connected compact Lie groups, drawing connections with Hochschild cohomology and equivariant homotopy theory. First, for a compact Lie group $G$, we show that the string topology…

Algebraic Topology · Mathematics 2007-11-10 Kate Gruher , Craig Westerland

Freedman proposes a family of Hamiltonians $H_{0,l}$ which define quantum loop gas models on any celluated compact surface. We study the simplest nontrivial cases: celluations of the torus. Our numerical data support Freedman's conjecture,…

Mathematical Physics · Physics 2007-05-23 James Brink , Zhenghan Wang

In this paper, we investigate the behaviour of the Serre spectral sequence with respect to the algebraic structures of string topology in generalized homology theories, specificially with the Chas-Sullivan product and the corresponding…

Algebraic Topology · Mathematics 2016-01-20 Lennart Meier

We consider the closure space on the set of strings of a gentle algebra of finite representation type. Palu, Pilaud, and Plamondon proved that the collection of all biclosed sets of strings forms a lattice, and moreover, that this lattice…

Representation Theory · Mathematics 2018-08-31 Alexander Garver , Thomas McConville , Kaveh Mousavand

Recently R. Cohen and V. Godin have proved that the homology of the free loop space of a closed oriented manifold with coefficients in a field has the structure of a Frobenius algebra without counit. In this short note we prove that when…

Algebraic Topology · Mathematics 2007-05-23 David Chataur , Jean-Claude Thomas

We describe an algebraic chain level construction that models the passage from an arbitrary topological space to its free loop space. The input of the construction is a categorical coalgebra, i.e. a curved coalgebra satisfying certain…

Algebraic Topology · Mathematics 2023-11-22 Manuel Rivera

We study the hamiltonian reduction of affine Lie superalgebra $sl(2|1)^{(1)}$. Based on a scalar Lax operator formalism, we derive the free field realization of the classical topological topological algebra which appears in the $c\leq1$…

High Energy Physics - Theory · Physics 2015-06-26 Katsushi Ito , Hiroaki Kanno

Sati and Schreiber [arXiv:2402.18473, arXiv:2512.12431] have proposed that charge quantisation in quantum field theory and string theory is governed by a homotopy type $\mathcal A$. We provide a refinement of this postulate, incorporating…

High Energy Physics - Theory · Physics 2026-05-22 Luigi Alfonsi , Hyungrok Kim , William G. A. Luciani

A Cartan decomposition for symmetric pairs plays an important role to study not only orbit geometry of the symmetric spaces but also harmonic analysis on them. For non-symmetric reductive pairs, there are examples of generalizations of…

Representation Theory · Mathematics 2019-11-18 Atsumu Sasaki

To give a Cartan calculus on the extended quantum 3d space, the noncommutative differential calculus on the extended quantum 3d space is extended by introducing inner derivations and Lie derivatives.

Quantum Algebra · Mathematics 2007-05-23 Salih Çelik , Ergün Yaşar , E. Mehmet Özkan